FRACTAL ROUGHNESS IN CONTACT PROBLEMS

The roughness of real polished bodies is shown to be fractal in charac ter. A relation is found between the fractal dimension of a surface an d its statistical properties. Models are constructed of the contact of fractal-rough punches and the smooth surface of a deformable half-spa ce by a modelling Winkler medium and a rigidly plastic medium. At the macrolevel, the impressed punches are regarded as either flat or conve x. At the initial stage of indentation, when the proximity of the punc h and the medium is much less than the size of irregularities, asympto tic power laws have been obtained which associate the force operating on the punch and the depth of indentation for different (both plastic and elastic) models of the deformed base. The relation between the pow er index and the fractal dimension of the surface and the print is det ermined.